Problem: Simplify to lowest terms. $\dfrac{70}{42}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 70 and 42? $70 = 2\cdot5\cdot7$ $42 = 2\cdot3\cdot7$ $\mbox{GCD}(70, 42) = 2\cdot7 = 14$ $\dfrac{70}{42} = \dfrac{5 \cdot 14}{ 3\cdot 14}$ $\hphantom{\dfrac{70}{42}} = \dfrac{5}{3} \cdot \dfrac{14}{14}$ $\hphantom{\dfrac{70}{42}} = \dfrac{5}{3} \cdot 1$ $\hphantom{\dfrac{70}{42}} = \dfrac{5}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{70}{42}= \dfrac{2\cdot35}{2\cdot21}= \dfrac{2\cdot 7\cdot5}{2\cdot 7\cdot3}= \dfrac{5}{3}$